Optimal streamlined bodies and the practical limits of tail-mounted boundary-layer-ingesting propulsion: a reduced-order and RANS study

We revisit two classical questions about bodies moving through a fluid at constant speed. First, which axisymmetric shape minimises the drag at fixed volume or at fixed frontal area? Second, how much propulsive power can be saved by placing the propulsor at the tail so that it ingests the body's boundary layer (boundary-layer ingestion, BLI, as in the Goldschmied body), and how large may the duct losses be before the saving disappears? A two-dimensional lattice-Boltzmann model, an axisymmetric panel/integral-boundary-layer model with shape optimisation, and axisymmetric RANS simulations (k-omega SST, OpenFOAM) are combined. The optimum is a conventional elongated teardrop, with fineness ratio L/D ≈ 3 at fixed frontal area and L/D ≈ 6 at fixed volume; with a turbulent boundary layer, axisymmetric golden-ratio bodies have 2.4-3.6 times the drag of the optimum. For a fully turbulent boundary layer the reduced-order model gives a break-even duct loss K* that decreases from 8.5% to 4.5% of the free-stream dynamic pressure as the volumetric Reynolds number goes from 3×10^5 to 10^8. RANS simulations at Re_V = 10^6 show that an unducted actuator disc ingesting the boundary layer needs 8–18% less power than the conventional reference, depending on the size of the reference propeller; a flush wall slot loses essentially all the ingested total pressure; and a well-designed ducted intake keeps the intake loss at about 2% but its power ranges from 2% below to 9% above the conventional reference, because cowl friction and flow acceleration cancel most or all of the BLI benefit. All codes and data are openly available. Version 2: transition criterion of the shape table stated (with the e^N sensitivity), abstract aligned with the tables, methods described explicitly and references added. The list of changes is in nota/CHANGES.md of the code repository (release v1.1.0).